Blown fuse, faulty flasher unit, or, like you said, turn signal switch. Does the flasher unit make a sound when you activate either of the turn signals? Also, keep in mind that when the hazard switch is 'activated,' it disables both turn signals. Food for thought.

Double check the hazard switch. I had to use mine not too long ago and afterwards my turn signals did not work at all. I pushed the hazard button and they came on so I turned it off then just like that the signals worked again. My switch was loose and caused that issue so maybe its worth looking at.

When I turn the blinkers on left or right, I get no flashing arrow on teh dash, no noise, and the lights outside don't do anything. However if I turn on the hazards, both green arrows in the dash blink, I get the noise, and all 4 corners outside flash.

did you check the blinker fluid resevoir? ive heard that for some reason these subarus like to eat it if not properly maintained.

This.
In fact, check the fluid line running from the reservoir to the front, passenger turn signal. I've found that on some cars, one of the plastic clips securing it to the firewall tends to come loose (or break, in my case) and allow the line to droop down low enough to rub against the steering shaft. You can rub a hole in it really easily because the line is very thin.